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Light tail asymptotics in multidimensional reflecting processes for queueing networks

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Abstract

We are concerned with the stationary distributions of reflecting processes on multidimensional nonnegative orthants and other related processes, provided they exist. Such stationary distributions arise in performance evaluation for various queueing systems and their networks. However, it is very hard to obtain them analytically, so our interest is directed to analytically tractable characteristics. For this, we consider tail asymptotics of the stationary distributions.

The purpose of this paper is twofold. We first overview the current approaches to attack the problem from a unified viewpoint. We then take up two approaches, Markov additive and analytic function approaches, which are recently developed by the author and his colleagues. We discuss their possible extensions. We mainly consider the tail asymptotics for two-dimensional reflecting processes, but also discuss how we can approach the case of more than two dimensions.

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  1. Tokyo University of Science, Noda, Chiba, 278-8510, Japan

    Masakiyo Miyazawa

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  1. Masakiyo Miyazawa
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Correspondence to Masakiyo Miyazawa.

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This invited paper is discussed in the comments available at doi:10.1007/s11750-011-0181-0, doi:10.1007/s11750-011-0182-z, doi:10.1007/s11750-011-0183-y, doi:10.1007/s11750-011-0184-x.

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Miyazawa, M. Light tail asymptotics in multidimensional reflecting processes for queueing networks. TOP 19, 233–299 (2011). https://doi.org/10.1007/s11750-011-0179-7

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